Copyright	(c) Edward Kmett 2010-2014
License	BSD3
Maintainer	ekmett@gmail.com
Stability	experimental
Portability	GHC only
Safe Haskell	None
Language	Haskell2010

Numeric.AD.Mode.Sparse

Contents

Sparse Gradients
Sparse Jacobians (synonyms)
Sparse Hessians

Description

Higher order derivatives via a "dual number tower".

Synopsis

Documentation

data AD s a Source

Instances

Bounded a => Bounded (AD s a)
Enum a => Enum (AD s a)
Eq a => Eq (AD s a)
Floating a => Floating (AD s a)
Fractional a => Fractional (AD s a)
Num a => Num (AD s a)
Ord a => Ord (AD s a)
Read a => Read (AD s a)
Real a => Real (AD s a)
RealFloat a => RealFloat (AD s a)
RealFrac a => RealFrac (AD s a)
Show a => Show (AD s a)
Erf a => Erf (AD s a)
InvErf a => InvErf (AD s a)
Mode a => Mode (AD s a)
Typeable (* -> * -> *) AD
type Scalar (AD s a) = Scalar a

data Sparse a Source

We only store partials in sorted order, so the map contained in a partial will only contain partials with equal or greater keys to that of the map in which it was found. This should be key for efficiently computing sparse hessians. there are only (n + k - 1) choose k distinct nth partial derivatives of a function with k inputs.

Instances

(Num a, Bounded a) => Bounded (Sparse a)
(Num a, Enum a) => Enum (Sparse a)
(Num a, Eq a) => Eq (Sparse a)
Floating a => Floating (Sparse a)
Fractional a => Fractional (Sparse a)
Data a => Data (Sparse a)
Num a => Num (Sparse a)
(Num a, Ord a) => Ord (Sparse a)
Real a => Real (Sparse a)
RealFloat a => RealFloat (Sparse a)
RealFrac a => RealFrac (Sparse a)
Show a => Show (Sparse a)
Erf a => Erf (Sparse a)
InvErf a => InvErf (Sparse a)
Num a => Mode (Sparse a)
Num a => Jacobian (Sparse a)
Num a => Grad (Sparse a) [a] (a, [a]) a
Num a => Grads (Sparse a) (Cofree [] a) a
Typeable (* -> *) Sparse
Grads i o a => Grads (Sparse a -> i) (a -> o) a
Grad i o o' a => Grad (Sparse a -> i) (a -> o) (a -> o') a
type Scalar (Sparse a) = a
type D (Sparse a) = Sparse a

auto :: Mode t => Scalar t -> t Source

Embed a constant

Sparse Gradients

grad :: (Traversable f, Num a) => (forall s. f (AD s (Sparse a)) -> AD s (Sparse a)) -> f a -> f a Source

grad' :: (Traversable f, Num a) => (forall s. f (AD s (Sparse a)) -> AD s (Sparse a)) -> f a -> (a, f a) Source

grads :: (Traversable f, Num a) => (forall s. f (AD s (Sparse a)) -> AD s (Sparse a)) -> f a -> Cofree f a Source

gradWith :: (Traversable f, Num a) => (a -> a -> b) -> (forall s. f (AD s (Sparse a)) -> AD s (Sparse a)) -> f a -> f b Source

gradWith' :: (Traversable f, Num a) => (a -> a -> b) -> (forall s. f (AD s (Sparse a)) -> AD s (Sparse a)) -> f a -> (a, f b) Source

Sparse Jacobians (synonyms)

jacobian :: (Traversable f, Functor g, Num a) => (forall s. f (AD s (Sparse a)) -> g (AD s (Sparse a))) -> f a -> g (f a) Source

jacobian' :: (Traversable f, Functor g, Num a) => (forall s. f (AD s (Sparse a)) -> g (AD s (Sparse a))) -> f a -> g (a, f a) Source

jacobianWith :: (Traversable f, Functor g, Num a) => (a -> a -> b) -> (forall s. f (AD s (Sparse a)) -> g (AD s (Sparse a))) -> f a -> g (f b) Source

jacobianWith' :: (Traversable f, Functor g, Num a) => (a -> a -> b) -> (forall s. f (AD s (Sparse a)) -> g (AD s (Sparse a))) -> f a -> g (a, f b) Source

jacobians :: (Traversable f, Functor g, Num a) => (forall s. f (AD s (Sparse a)) -> g (AD s (Sparse a))) -> f a -> g (Cofree f a) Source

Sparse Hessians

hessian :: (Traversable f, Num a) => (forall s. f (AD s (Sparse a)) -> AD s (Sparse a)) -> f a -> f (f a) Source

hessian' :: (Traversable f, Num a) => (forall s. f (AD s (Sparse a)) -> AD s (Sparse a)) -> f a -> (a, f (a, f a)) Source

hessianF :: (Traversable f, Functor g, Num a) => (forall s. f (AD s (Sparse a)) -> g (AD s (Sparse a))) -> f a -> g (f (f a)) Source

hessianF' :: (Traversable f, Functor g, Num a) => (forall s. f (AD s (Sparse a)) -> g (AD s (Sparse a))) -> f a -> g (a, f (a, f a)) Source